Challenging Physics Problems

This is a sample of the problems from the book “200 Puzzling Physics Problems” published by Cambridge University Press:

http://catdir.loc.gov/catdir/sam ples/cam034/00053005.pdf

This above resource contains 89 of the problems, but no solutions.

The problems here are simple to state, but seem to get at profound mathematical and physical ideas.  For example, if the Earth and Sun were scaled down as to be 1 meter apart on average, how long would a year be?

I can see a lot of productive student struggle coming from this book!

Fibonacci Flushers

While travelling in Europe, I became fascinated with the variety of toilet-flushing mechanisms I encountered.  The typical toilet had a low-flow / high-flow option (which I imagine saves a great deal of water in the long run) , and a lot of creativity emerged in the way this two-flush system was implemented.

While documenting the many ways to flush, I found this rectangular model oddly familiar and appealing.

And then it hit me:  this looks like the golden rectangle!

The golden ratio has long been used by artists and architects to create aesthetically pleasing work.  It is, after all, the divine proportion.  Could it be that these toilet-makers took their cues from the masters of art and math?  I had to find out.

I dropped my image into Geogebra and took some measurements.

The total length of the rectangle divided by its height is around 1.71.  So, it’s not quite the golden ratio, but it’s pretty close.  This flush-design is about 90% divine, I suppose.

Maybe their next design will be closer to the perfect proportion.

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